1.To be conscious is to be conscious of.....something.
2.The law of identity: To be is to be.....something.
3.Existence IS identity.
4.Existence differentiates a "thing" from nothing.
Existence and Identity are axiomatic concepts. They cannot be further reduced or defined.
Incidentally, a consciousness with nothing to be conscious "of" is a contradiction in terms. Before it could identify itself AS consciousness, it had to be conscious of something. If that which you claim to perceive does not exist, what you possess is not consciousness.
Existence and identity are not attributes of existents, they ARE the existents!
The unreal does not exist; the unreal is merely that negation of existence which is the content of a human consciousness when it attempts to ABANDON reason.